"""simple docstring"""







import random



def      lowercase__(			__SCREAMING_SNAKE_CASE				:	list	,     __SCREAMING_SNAKE_CASE				:	List[str] ):
     lowercase_      :							List[str]						=      [], [], []
     for element in data:
          if element < pivot:
               less.append(__SCREAMING_SNAKE_CASE )
          elif element > pivot:
               greater.append(__SCREAMING_SNAKE_CASE )
          else:
               equal.append(__SCREAMING_SNAKE_CASE )
     return less, equal, greater







def      lowercase__(			__SCREAMING_SNAKE_CASE				:	list	,     __SCREAMING_SNAKE_CASE				:	int ):
     # index = len(items) // 2 when trying to find the median
     #   (value of index when items is sorted)

     # invalid input
     if index >= len(__SCREAMING_SNAKE_CASE ) or index < 0:
          return None

     lowercase_      :							List[Any]						=      items[random.randint(0	,     len(__SCREAMING_SNAKE_CASE ) - 1 )]
     lowercase_      :							Optional[Any]						=      0
     lowercase_      :							Any						=      _partition(__SCREAMING_SNAKE_CASE	,     __SCREAMING_SNAKE_CASE )
     lowercase_      :							Union[str, Any]						=      len(__SCREAMING_SNAKE_CASE )
     lowercase_      :							List[Any]						=      len(__SCREAMING_SNAKE_CASE )

     # index is the pivot
     if m <= index < m + count:
          return pivot
     # must be in smaller
     elif m > index:
          return quick_select(__SCREAMING_SNAKE_CASE	,     __SCREAMING_SNAKE_CASE )
     # must be in larger
     else:
          return quick_select(__SCREAMING_SNAKE_CASE	,     index - (m + count) )









'''simple docstring'''





from __future__ import annotations

import os
from collections.abc import Mapping

_UpperCamelCase						:						Any  =					tuple[int, int]


class  snake_case__      :




					def __init__(  self  :		List[str]				, _A  :		set[int]				, _A  :		Mapping[EdgeT, int]      )    ->							None:
								UpperCAmelCase_      :       set[int]          =       vertices
								UpperCAmelCase_      :       dict[EdgeT, int]          =       {
								    (min(_A      ), max(_A      )): weight for edge, weight in edges.items()
								}




					def 		A      (  self  :		Union[str, Any]				, _A  :		EdgeT				, _A  :		int      )    ->							None:
								self.vertices.add(edge[0]      )
								self.vertices.add(edge[1]      )
								UpperCAmelCase_      :       List[str]          =       weight





					def 		A      (  self  :		str      )    ->							Graph:
								UpperCAmelCase_      :       Graph          =       Graph({min(self.vertices      )}				, {}      )
								UpperCAmelCase_      :       EdgeT
								UpperCAmelCase_      :       int
								UpperCAmelCase_      :       EdgeT
								UpperCAmelCase_      :       int

								while len(subgraph.vertices      ) < len(self.vertices      ):
											UpperCAmelCase_      :       Optional[Any]          =       max(self.edges.values()      ) + 1
											for edge, weight in self.edges.items():
														if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
																	if weight < min_weight:
																				UpperCAmelCase_      :       Dict          =       edge
																				UpperCAmelCase_      :       Tuple          =       weight

											subgraph.add_edge(_A				, _A      )

								return subgraph






def __UpperCAmelCase   (					A					:			str = "p107_network.txt"		)    ->   int:
			UpperCAmelCase_      :       str          =       os.path.abspath(os.path.dirname(A		)		)
			UpperCAmelCase_      :       str          =       os.path.join(A			,       A		)
			UpperCAmelCase_      :       dict[EdgeT, int]          =       {}
			UpperCAmelCase_      :       list[str]
			UpperCAmelCase_      :       int
			UpperCAmelCase_      :       int

			with open(A		) as f:
						UpperCAmelCase_      :       int          =       f.read().strip().split('''\n'''		)

			UpperCAmelCase_      :       Any          =       [line.split(''','''		) for line in data]

			for edgea in range(1			,       len(A		)		):
						for edgea in range(A		):
									if adjaceny_matrix[edgea][edgea] != "-":
												UpperCAmelCase_      :       Optional[int]          =       int(adjaceny_matrix[edgea][edgea]		)

			UpperCAmelCase_      :       Graph          =       Graph(set(range(len(A		)		)		)			,       A		)

			UpperCAmelCase_      :       Graph          =       graph.prims_algorithm()

			UpperCAmelCase_      :       int          =       sum(graph.edges.values()		)
			UpperCAmelCase_      :       int          =       sum(subgraph.edges.values()		)

			return initial_total - optimal_total


if __name__ == "__main__":
						print(f'''{solution() = }''')


